Category: Limits

Question Number 89341 by Henri Boucatchou last updated on 17/Apr/20 $$\underset{n\to \mathrm{\infty }}{lim}\sqrt[n]{\underset{k=1}{\prod ^{n-1}}sin\left(\frac{k\pi }{2n}\right)}=?$$ Commented by Henri Boucatchou last updated on 17/Apr/20 $$\boldsymbol{{Check}}\:\:\boldsymbol{{once}}\:\:\boldsymbol{{more}}\:\:\boldsymbol{{Sir}},\:\:\:\boldsymbol{{ln}}\underset{{i}}…

Question Number 23764 by Anoop kumar last updated on 05/Nov/17 $$\text{Missing left or extra right}$$$$wheren\epsilon N$$$$…

Question Number 154776 by john_santu last updated on 21/Sep/21 $$\underset{x\to \mathrm{\infty }}{\lim }{(1+\frac{1-\frac{\sin \left(\frac{1}{x}\right)}{\frac{1}{x}}}{e-{(1+\frac{1}{x})}^x})}^x=?$$ Commented by mathdanisur last updated on 21/Sep/21 $$\mathrm{say}\frac{1}{\mathrm{x}}=\mathrm{t}\Rightarrow \mathrm{t}\to 0$$$$\mathrm{e}^{\underset{\boldsymbol{\mathrm{t}}\rightarrow\mathrm{0}}…

Question Number 154719 by liberty last updated on 21/Sep/21 $$\underset{x\to \frac{\pi }{6}}{\lim }\frac{2\ln \left[\mathrm{\Gamma }\left(\sin x\right)\right]-\ln \pi }{\mathrm{\Gamma }\left(\sec x\right)-1}=?$$ Answered by john_santu last updated on 21/Sep/21 $$\:\underset{{x}\rightarrow\frac{\pi}{\mathrm{6}}} {\mathrm{lim}}\:\frac{\mathrm{2cos}\:{x}\:\Psi^{\mathrm{0}} \left(\mathrm{sin}\:\left({x}\right)\right)}{\mathrm{2tan}\:\left(\mathrm{2}{x}\right)\mathrm{sec}\:\left(\mathrm{2}{x}\right)\Gamma\left(\mathrm{sec}\:\left(\mathrm{2}{x}\right)\right)\Psi^{\mathrm{0}} \left(\mathrm{sec}\:\left(\mathrm{2}{x}\right)\right)}= \…

Question Number 154652 by EDWIN88 last updated on 20/Sep/21 $$\underset{x\to 0}{\lim }\frac{1-\tan (x+\frac{\pi }{4})\tan (2x+\frac{\pi }{4})\tan (\frac{\pi }{4}-3x)}{x^3}=?$$ Answered by bramlexs22 last updated on 20/Sep/21 Commented by mnjuly1970 last…